Discrete mode observability of structured switching descriptor linear systems: A graph-theoretic approach

The main result of the paper consists in necessary and sufficient graphical conditions which ensure the generic discrete mode observability of structured switching descriptor systems. The methods used in the previous studies on the observability of switching linear systems on standard form are not applicable to switching descriptor systems. So, we develop a new approach starting from bipartite representations of these systems and then building a new kind of digraph dedicated to the discrete mode observability study. The proposed method assumes only the knowledge of the system’s structure and is applicable to a large class of descriptor systems including regular and non-regular systems even if they are square or under-determined. The provided conditions can be implemented by the classical graph-theory algorithms.